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.TH ell1mag 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
ell1mag - magnitude of elliptic filter
.SH CALLING SEQUENCE
.nf
[v]=ell1mag(eps,m1,z)
.fi
.SH PARAMETERS
.TP 10
eps
: passband ripple=\fV1/(1+eps^2)\fR
.TP
m1
: stopband ripple=\fV1/(1+(eps^2)/m1)\fR
.TP
z
: sample vector of values in the complex plane
.TP
v
: elliptic filter values at sample points
.SH DESCRIPTION
Function used for squared magnitude of an elliptic filter.
Usually \fVm1=eps*eps/(a*a-1)\fR. Returns
\fVv=real(ones(z)./(ones(z)+eps*eps*s.*s))\fR for \fVs=%sn(z,m1)\fR.
.SH EXAMPLE
.nf
deff('[alpha,beta]=alpha_beta(n,m,m1)',...
'if 2*int(n/2)=n then, beta=K1; else, beta=0;end;...
alpha=%k(1-m1)/%k(1-m);')
epsilon=0.1;A=10; //ripple parameters
m1=(epsilon*epsilon)/(A*A-1);n=5;omegac=6;
m=find_freq(epsilon,A,n);omegar = omegac/sqrt(m)
%k(1-m1)*%k(m)/(%k(m1)*%k(1-m))-n //Check...
[alpha,beta]=alpha_beta(n,m,m1)
alpha*%asn(1,m)-n*%k(m1) //Check
sample=0:0.01:20;
//Now we map the positive real axis into the contour...
z=alpha*%asn(sample/omegac,m)+beta*ones(sample);
plot(sample,ell1mag(epsilon,m1,z))
.fi
.SH SEE ALSO
buttmag
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